Best Known (106−36, 106, s)-Nets in Base 7
(106−36, 106, 192)-Net over F7 — Constructive and digital
Digital (70, 106, 192)-net over F7, using
- trace code for nets [i] based on digital (17, 53, 96)-net over F49, using
- net from sequence [i] based on digital (17, 95)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- F4 from the tower of function fields by GarcÃa, Stichtenoth, and Rück over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- net from sequence [i] based on digital (17, 95)-sequence over F49, using
(106−36, 106, 858)-Net over F7 — Digital
Digital (70, 106, 858)-net over F7, using
(106−36, 106, 119295)-Net in Base 7 — Upper bound on s
There is no (70, 106, 119296)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 380540 497490 235086 277256 002778 640641 190626 955114 365204 972787 141790 863335 217292 159779 331073 > 7106 [i]